Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}4x-2y &= -8 \\ -x+9y &= 2\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $9y = x+2$ Divide both sides by $9$ to isolate $y$ $y = {\dfrac{1}{9}x + \dfrac{2}{9}}$ Substitute this expression for $y$ in the first equation. $4x-2({\dfrac{1}{9}x + \dfrac{2}{9}}) = -8$ $4x - \dfrac{2}{9}x - \dfrac{4}{9} = -8$ Simplify by combining terms, then solve for $x$ $\dfrac{34}{9}x - \dfrac{4}{9} = -8$ $\dfrac{34}{9}x = -\dfrac{68}{9}$ $x = -2$ Substitute $-2$ for $x$ back into the top equation. $4( -2)-2y = -8$ $-8-2y = -8$ $-2y = 0$ $y = 0$ The solution is $\enspace x = -2, \enspace y = 0$.